Testing central assumptions of trait-based ecology
Appendix
2022-12-19
- 1 Background
- 2 Compare Models
- 2.1 Model 1: Tree Age + Plant Trait +
Environmental Conditions
- 2.1.1 Model Parameters
- 2.1.2 Build Model
- 2.1.3 Relative Importance
- 2.1.4 Partial Dependence
- 2.1.5 Performance
- 2.1.6 Interactions | Table
- 2.1.7 Interaction | Group | Test
- 2.1.8 Interaction | Group | Violin
- 2.1.9 Interaction | Group | Boxplot
- 2.1.10 Interaction | Group | Density
- 2.1.11 Interaction | Group | Top
- 2.1.12 Interactions | Plots
- 2.1.13 Group Relative Importance
- 2.2 Model 2: Tree Age + Species
Identity + Environmental Conditions
- 2.2.1 Model Parameters
- 2.2.2 Build Model
- 2.2.3 Relative Importance
- 2.2.4 Partial Dependence
- 2.2.5 Performance
- 2.2.6 Interactions | Table
- 2.2.7 Interaction | Group | Test
- 2.2.8 Interaction | Group | Violin
- 2.2.9 Interaction | Group | Boxplot
- 2.2.10 Interaction | Group | Density
- 2.2.11 Interactions | Plots
- 2.2.12 Group Relative Importance
- 2.3 Model 3: Tree Age + Species
Identity + Plant Trait + Environmental Conditions
- 2.3.1 Model Parameters
- 2.3.2 Build Model
- 2.3.3 Relative Importance
- 2.3.4 Partial Dependence
- 2.3.5 Performance
- 2.3.6 Interactions | Table
- 2.3.7 Interaction | Group | Test
- 2.3.8 Interaction | Group | Violin
- 2.3.9 Interaction | Group | Boxplot
- 2.3.10 Interaction | Group | Density
- 2.3.11 Interactions | Plots
- 2.3.12 Group Relative Importance
- 2.1 Model 1: Tree Age + Plant Trait +
Environmental Conditions
1 Background
We hope to explore the relative influence of physical traits, environmental conditions and species identity on the growth rate of trees. A gradient boosted model seems like a good candidate for this work since they:
- Can effectively model interactions, without the modeler specifying them
- Do not drop rows with NAs - these rows are put into their own node (i.e., na.action = na.pass)
- Can effectively model non-linear relationships - these are quite likely in the relationship between growth rate and the predictors. The GBM can help us understand them, but it can also model them.
1.1 Extracting Principle Components for Environmental Traits
We, first, converted the environmental variables to principle
components as they were highly correlated. We visualized the PCA and
used the eginvectors to help figure which environmental condition best
explained that PC. There were 5 -
Soil Fertility, Light, Temperature, pH, Soil.Humidity.Depth, and Slope.
1.1.1 PC1-PC2
1.1.2 P3-PC4
1.1.3 PC5-PC6
1.1.4 Correlation on Plant Traits
We want to ensure that the plant traits are not correlated. Past work suggests that they are not easily represented using a PCA. So, we will not use the this feature reduction method.
1.2 About Gradient Boosted Models
A gradient boosted machine/model is a machine learning model that uses decision trees to fit the data.
A decision tree first starts with all of the observations, then, from the variables provided, it tries to figure out which variable split would result in the “purest” groupings of the data. So, in this case, it would try to place rows with higher growth rates in one node, and those with lower growth rates in another node.
GBMs are an ensemble of decision trees, nut they are fit
sequentially. We call GBMs an ensemble of weak learners as each
subsequent tree is an attempt to correct the errors of the previous
tree. Thus, while one tree, by itself, can not describe the
relationships, with the use of all the trees, we can. Below is a figure
by Bradly Bohemke that attempts to illustrate how each subsequent tree
improves the fit on the data. 
2 Compare Models
We compared the fit of three used a gradient boosted models to determine how environmental gradients and physical traits influence RGR:
- Model 1 (Plant Traits + Environmental Conditions + Tree Age): this model assumes that in additional to tree age, growth rates are best described by the traits of the tree and environmental conditions.
- Model 2 (Species Identity + Environmental Conditions + Tree Age): it is possible that species identity is a stronger predictor of growth rates than the traits of the tree. As such, in this model, we ignore plant traits and use species identity.
- Model 3 (Species Identity + Plant Traits + Environmental Conditions + Tree Age): here, we hypothesize that while plant traits and environmental conditions are influential, we may have greater predictive power if we also consider the species of the tree.
2.1 Model 1: Tree Age + Plant Trait + Environmental Conditions
2.1.1 Model Parameters
First, we look at the best parameters from tuning.
## $model_id
## [1] "final_grid_model_57"
##
## $training_frame
## [1] "train.hex"
##
## $validation_frame
## [1] "valid.hex"
##
## $score_tree_interval
## [1] 10
##
## $ntrees
## [1] 10000
##
## $max_depth
## [1] 11
##
## $min_rows
## [1] 1
##
## $nbins
## [1] 16
##
## $nbins_cats
## [1] 256
##
## $stopping_rounds
## [1] 5
##
## $stopping_metric
## [1] "MSE"
##
## $stopping_tolerance
## [1] 1e-04
##
## $max_runtime_secs
## [1] 3395.824
##
## $seed
## [1] 1234
##
## $learn_rate
## [1] 0.05
##
## $learn_rate_annealing
## [1] 0.99
##
## $distribution
## [1] "gaussian"
##
## $sample_rate
## [1] 0.49
##
## $col_sample_rate
## [1] 0.42
##
## $col_sample_rate_per_tree
## [1] 0.34
##
## $min_split_improvement
## [1] 1e-08
##
## $histogram_type
## [1] "UniformAdaptive"
##
## $categorical_encoding
## [1] "Enum"
##
## $calibration_method
## [1] "PlattScaling"
##
## $x
## [1] "Soil.Fertility" "Light" "Temperature" "pH" "Slope"
## [6] "Estem" "Branching.Distance" "Stem.Wood.Density" "Leaf.Area" "LMA"
## [11] "LCC" "LNC" "LPC" "d15N" "t.b2"
## [16] "Ks" "Ktwig" "Huber.Value" "X.Lum" "VD"
## [21] "X.Sapwood" "d13C" "Tree.Age" "julian.date.2011"
##
## $y
## [1] "BAI_GR"2.1.2 Build Model
Now, we can build the model.
set.seed(123)
gbm_regressor_bai_residuals <-
gbm(BAI_GR ~ .,
data =
rgr_msh_na %>% filter(Group == "Train")%>% filter(!is.na(BAI_GR))%>%
select(any_of(c(EnvironmentalVariablesKeep, PlantTraitsKeep, "Tree.Age", "BAI_GR", "julian.date.2011"))),
n.trees = 1000,
interaction.depth = 11, #max depth
shrinkage = 0.05, #learning rate
n.minobsinnode = 10, #col_sample_rate
bag.fraction = 0.49, # sample_rate,
verbose = FALSE,
n.cores = NULL,
cv.folds = 5)2.1.3 Relative Importance
First, we look at the importance of variables in the model.
2.1.4 Partial Dependence
Assessing how, when we hold everything else constant, what the relationships are between growth rate and the predictor.
Soil Fertility
Light
Temperature
pH
Slope
Modulus of Elasticity for Stem
Branching Distance
Stem Wood Density
Leaf Area
Leaf Mass Per Area
Leaf Carbon Concentration
Leaf Nitrogen Concentration
Leaf Phosphorus Concentration
Delta 15N
Thickness to Span Ratio
Conductivity Per Sapwood Area
Conductivity per Branch
Huber Value
Percent Lumen
Vessel Diameter
Percent Sapwood
Delta 13C
Tree Age
Julian Date in 2011
2.1.5 Performance
How does the model perform when we use the true individual trait value?
2.1.6 Interactions | Table
Let’s explore the interactions in these data.
2.1.7 Interaction | Group | Test
##
## Kruskal-Wallis rank sum test
##
## data: Value by Class
## Kruskal-Wallis chi-squared = 21.524, df = 3, p-value = 8.194e-05## Comparison Z P.unadj
## 1 Environmental Conditions:Environmental Conditions - Environmental Conditions:Plant Traits 0.5730733 5.665950e-01
## 2 Environmental Conditions:Environmental Conditions - Plant Traits:Environmental Conditions -2.9581361 3.095055e-03
## 3 Environmental Conditions:Plant Traits - Plant Traits:Environmental Conditions -1.7512647 7.990033e-02
## 4 Environmental Conditions:Environmental Conditions - Plant Traits:Plant Traits -4.2940685 1.754283e-05
## 5 Environmental Conditions:Plant Traits - Plant Traits:Plant Traits -2.2793383 2.264696e-02
## 6 Plant Traits:Environmental Conditions - Plant Traits:Plant Traits -1.4936179 1.352755e-01
## P.adj
## 1 0.566595039
## 2 0.015475273
## 3 0.239700984
## 4 0.000105257
## 5 0.090587842
## 6 0.2705510582.1.8 Interaction | Group | Violin
2.1.9 Interaction | Group | Boxplot
2.1.10 Interaction | Group | Density
2.1.11 Interaction | Group | Top
2.1.12 Interactions | Plots
Now, we plot interactions with values>0.10.
Leaf Phosphorus Concentration:Huber Value
Leaf Phosphorus Concentration:Percent Lumen
Percent Lumen:Tree Age
Leaf Phosphorus Concentration:Tree Age
Leaf Area:Thickness to Span Ratio
Light:Branching Distance
Soil Fertility:Huber Value
Slope:Vessel Diameter
Leaf Area:Huber Value
Modulus of Elasticity for Stem:Delta 13C
Branching Distance:Leaf Nitrogen Concentration
Delta 15N:Huber Value
Leaf Phosphorus Concentration:Vessel Diameter
pH:Conductivity per Branch
Slope:Modulus of Elasticity for Stem
Soil Fertility:Temperature
Thickness to Span Ratio:Vessel Diameter
Light:Conductivity per Branch
Leaf Carbon Concentration:Tree Age
Soil Fertility:Branching Distance
Slope:Tree Age
Branching Distance:Huber Value
Delta 15N:Delta 13C
Percent Sapwood:Tree Age
Thickness to Span Ratio:Percent Sapwood
Temperature:Branching Distance
Light:Tree Age
Modulus of Elasticity for Stem:Delta 15N
Branching Distance:Delta 15N
Leaf Mass Per Area:Modulus of Elasticity for Stem
Leaf Nitrogen Concentration:Percent Lumen
Modulus of Elasticity for Stem:Huber Value
Slope:Huber Value
Branching Distance:Julian Date in 2011
Branching Distance:Percent Lumen
Huber Value:Percent Lumen
Vessel Diameter:Percent Sapwood
Leaf Phosphorus Concentration:Conductivity Per Sapwood Area
Thickness to Span Ratio:Huber Value
Thickness to Span Ratio:Tree Age
Modulus of Elasticity for Stem:Branching Distance
pH:Leaf Nitrogen Concentration
Leaf Nitrogen Concentration:Thickness to Span Ratio
Branching Distance:Leaf Carbon Concentration
Temperature:Delta 13C
Modulus of Elasticity for Stem:Conductivity per Branch
Huber Value:Tree Age
Huber Value:Delta 13C
Branching Distance:Tree Age
2.1.13 Group Relative Importance
Finally, we compare the relative importance of the various groups - tree age, plant traits, and environmental conditions.
2.2 Model 2: Tree Age + Species Identity + Environmental Conditions
2.2.1 Model Parameters
First, we look at the best parameters from tuning.
## $model_id
## [1] "final_grid_model_64"
##
## $training_frame
## [1] "train.hex"
##
## $validation_frame
## [1] "valid.hex"
##
## $score_tree_interval
## [1] 10
##
## $ntrees
## [1] 10000
##
## $max_depth
## [1] 9
##
## $min_rows
## [1] 4
##
## $nbins
## [1] 1024
##
## $nbins_cats
## [1] 32
##
## $stopping_rounds
## [1] 5
##
## $stopping_metric
## [1] "MSE"
##
## $stopping_tolerance
## [1] 1e-04
##
## $max_runtime_secs
## [1] 3488.306
##
## $seed
## [1] 1234
##
## $learn_rate
## [1] 0.05
##
## $learn_rate_annealing
## [1] 0.99
##
## $distribution
## [1] "gaussian"
##
## $sample_rate
## [1] 0.74
##
## $col_sample_rate
## [1] 0.94
##
## $col_sample_rate_per_tree
## [1] 0.99
##
## $min_split_improvement
## [1] 0
##
## $histogram_type
## [1] "RoundRobin"
##
## $categorical_encoding
## [1] "Enum"
##
## $calibration_method
## [1] "PlattScaling"
##
## $x
## [1] "Soil.Fertility" "Light" "Temperature" "pH" "Slope" "Species"
## [7] "Tree.Age" "julian.date.2011"
##
## $y
## [1] "BAI_GR"2.2.2 Build Model
Now, we can build the model.
set.seed(123)
gbm_regressor_bai_residuals_species <-
gbm(BAI_GR ~ .,
data =
rgr_msh_na %>% filter(Group == "Train")%>% filter(!is.na(BAI_GR))%>%
select(any_of(c(EnvironmentalVariablesKeep, "Species", "Tree.Age", "BAI_GR", "julian.date.2011"))) %>%
mutate(Species = factor(Species)),
n.trees = 1000,
interaction.depth = 9, # max depth
shrinkage = 0.05, #learning rate
n.minobsinnode = 7, #col_sample_rate
bag.fraction = 0.74, # sample_rate,
verbose = FALSE,
n.cores = NULL,
cv.folds = 5)2.2.3 Relative Importance
First, we look at the importance of variables in the model.
2.2.4 Partial Dependence
Assessing how, when we hold everything else constant, what the relationships are between growth rate and the predictor.
Soil Fertility
Light
Temperature
pH
Slope
Species
Tree Age
Julian Date in 2011
2.2.5 Performance
How does the model perform?
2.2.6 Interactions | Table
Let’s explore the interactions in these data.
2.2.7 Interaction | Group | Test
##
## Kruskal-Wallis rank sum test
##
## data: Value by Class
## Kruskal-Wallis chi-squared = 3.6714, df = 3, p-value = 0.29922.2.8 Interaction | Group | Violin
2.2.9 Interaction | Group | Boxplot
2.2.10 Interaction | Group | Density
2.2.11 Interactions | Plots
Now, we plot interactions with values>0.10.
Species:Tree Age
Slope:Species
pH:Species
Temperature:Species
Species:Julian Date in 2011
Light:Species
Soil Fertility:pH
Soil Fertility:Species
Light:Tree Age
Soil Fertility:Light
Temperature:pH
Soil Fertility:Julian Date in 2011
Tree Age:Julian Date in 2011
pH:Slope
Temperature:Slope
Soil Fertility:Slope
Temperature:Julian Date in 2011
Light:Temperature
Slope:Tree Age
Soil Fertility:Temperature
2.2.12 Group Relative Importance
Finally, we compare the relative importance of the various groups - tree age, plant traits, and environmental conditions.
2.3 Model 3: Tree Age + Species Identity + Plant Trait + Environmental Conditions
2.3.1 Model Parameters
First, we look at the best parameters from tuning.
## $model_id
## [1] "final_grid_model_61"
##
## $training_frame
## [1] "train.hex"
##
## $validation_frame
## [1] "valid.hex"
##
## $score_tree_interval
## [1] 10
##
## $ntrees
## [1] 10000
##
## $max_depth
## [1] 9
##
## $min_rows
## [1] 4
##
## $nbins
## [1] 16
##
## $nbins_cats
## [1] 64
##
## $stopping_rounds
## [1] 5
##
## $stopping_metric
## [1] "MSE"
##
## $stopping_tolerance
## [1] 1e-04
##
## $max_runtime_secs
## [1] 3510.497
##
## $seed
## [1] 1234
##
## $learn_rate
## [1] 0.05
##
## $learn_rate_annealing
## [1] 0.99
##
## $distribution
## [1] "gaussian"
##
## $sample_rate
## [1] 0.49
##
## $col_sample_rate
## [1] 0.86
##
## $col_sample_rate_per_tree
## [1] 0.44
##
## $min_split_improvement
## [1] 1e-06
##
## $histogram_type
## [1] "QuantilesGlobal"
##
## $categorical_encoding
## [1] "Enum"
##
## $calibration_method
## [1] "PlattScaling"
##
## $x
## [1] "Soil.Fertility" "Light" "Temperature" "pH" "Slope"
## [6] "Estem" "Branching.Distance" "Stem.Wood.Density" "Leaf.Area" "LMA"
## [11] "LCC" "LNC" "LPC" "d15N" "t.b2"
## [16] "Ks" "Ktwig" "Huber.Value" "X.Lum" "VD"
## [21] "X.Sapwood" "d13C" "Species" "Tree.Age" "julian.date.2011"
##
## $y
## [1] "BAI_GR"2.3.2 Build Model
Now, we can build the model.
set.seed(123)
gbm_regressor_baiSpeciesAgeEP <-
gbm(BAI_GR ~ .,
data =
rgr_msh_na %>% filter(Group == "Train")%>% filter(!is.na(BAI_GR))%>%
select(any_of(c(EnvironmentalVariablesKeep, PlantTraitsKeep,"Species" ,
"Tree.Age", "BAI_GR", "julian.date.2011")))%>%
mutate(Species = factor(Species)),
n.trees = 1000,
interaction.depth = 9, #max depth
shrinkage = 0.05, #learning rate
n.minobsinnode = 21, #col_sample_rate
bag.fraction = 0.49, # sample_rate,
verbose = FALSE,
n.cores = NULL,
cv.folds = 5)2.3.3 Relative Importance
First, we look at the importance of variables in the model.
2.3.4 Partial Dependence
Assessing how, when we hold everything else constant, what the relationships are between growth rate and the predictor.
Soil Fertility
Light
Temperature
pH
Slope
Modulus of Elasticity for Stem
Branching Distance
Stem Wood Density
Leaf Area
Leaf Mass Per Area
Leaf Carbon Concentration
Leaf Nitrogen Concentration
Leaf Phosphorus Concentration
Delta 15N
Thickness to Span Ratio
Conductivity Per Sapwood Area
Conductivity per Branch
Huber Value
Percent Lumen
Vessel Diameter
Percent Sapwood
Delta 13C
Species
Tree Age
Julian Date in 2011
2.3.5 Performance
How does the model perform?
2.3.6 Interactions | Table
Let’s explore the interactions in these data.
2.3.7 Interaction | Group | Test
##
## Kruskal-Wallis rank sum test
##
## data: Value by Class
## Kruskal-Wallis chi-squared = 32.442, df = 3, p-value = 4.224e-072.3.8 Interaction | Group | Violin
2.3.9 Interaction | Group | Boxplot
2.3.10 Interaction | Group | Density
2.3.11 Interactions | Plots
Now, we plot interactions with values>0.10
Slope:Vessel Diameter
Light:Branching Distance
Temperature:Branching Distance
Branching Distance:Leaf Phosphorus Concentration
Light:Delta 13C
Temperature:Leaf Phosphorus Concentration
2.3.12 Group Relative Importance
Finally, we compare the relative importance of the various groups - tree age, plant traits, and environmental conditions.